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A Warehouse-Location Problem

Author

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  • William J. Baumol

    (Princeton University, Princeton, New Jersey)

  • Philip Wolfe

    (The Rand Corporation, Santa Monica, California)

Abstract

This paper describes a method for determining a more profitable geographic location pattern for the warehouses that are employed by a firm in delivering known quantities of its finished product to its customers, where the number of warehouses is also permitted to vary. It is shown that this can normally be expected to be a concave minimization problem. Unfortunately, there are usually no practical computational methods for determining the values of the variables that correspond to the absolute minimum of a concave cost function. However, a local optimum can be determined by a method described in the article. The method involves a sequence of transportation computations that are shown to converge to the solution. An illustrative small scale computation is included. An appendix explains in intuitive terms the nature of the computational difficulties that arise in a concave-programming problem.

Suggested Citation

  • William J. Baumol & Philip Wolfe, 1958. "A Warehouse-Location Problem," Operations Research, INFORMS, vol. 6(2), pages 252-263, April.
    • Handle: RePEc:inm:oropre:v:6:y:1958:i:2:p:252-263
    DOI: 10.1287/opre.6.2.252
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    Cited by:

    1. Zhalechian, M. & Tavakkoli-Moghaddam, R. & Zahiri, B. & Mohammadi, M., 2016. "Sustainable design of a closed-loop location-routing-inventory supply chain network under mixed uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 89(C), pages 182-214.
    2. Min, Hokey & Melachrinoudis, Emanuel, 1999. "The relocation of a hybrid manufacturing/distribution facility from supply chain perspectives: a case study," Omega, Elsevier, vol. 27(1), pages 75-85, February.
    3. Chung-Piaw Teo & Jia Shu, 2004. "Warehouse-Retailer Network Design Problem," Operations Research, INFORMS, vol. 52(3), pages 396-408, June.
    4. V. Balachandran & Suresh Jain, 1975. "Optimal Facility Location under Random Demand with General Cost Structure," Discussion Papers 149, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. Boussemart, Jean-Philippe & Leleu, Hervé & Shen, Zhiyang & Vardanyan, Michael & Zhu, Ning, 2019. "Decomposing banking performance into economic and credit risk efficiencies," European Journal of Operational Research, Elsevier, vol. 277(2), pages 719-726.
    6. Ross, Anthony & Khajehnezhad, Milad & Otieno, Wilkistar & Aydas, Osman, 2017. "Integrated location-inventory modelling under forward and reverse product flows in the used merchandise retail sector: A multi-echelon formulation," European Journal of Operational Research, Elsevier, vol. 259(2), pages 664-676.
    7. Liu, Kaijun & Zhou, Yonghong & Zhang, Zigang, 2010. "Capacitated location model with online demand pooling in a multi-channel supply chain," European Journal of Operational Research, Elsevier, vol. 207(1), pages 218-231, November.
    8. Sina Nayeri & Mahdieh Tavakoli & Mehrab Tanhaeean & Fariborz Jolai, 2022. "A robust fuzzy stochastic model for the responsive-resilient inventory-location problem: comparison of metaheuristic algorithms," Annals of Operations Research, Springer, vol. 315(2), pages 1895-1935, August.
    9. Lin, Dung-Ying & Tsai, Yu-Yun, 2014. "The ship routing and freight assignment problem for daily frequency operation of maritime liner shipping," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 67(C), pages 52-70.
    10. Badri, Masood A., 1999. "Combining the analytic hierarchy process and goal programming for global facility location-allocation problem," International Journal of Production Economics, Elsevier, vol. 62(3), pages 237-248, September.
    11. Mateusz Żotkiewicz & Mariusz Mycek & Artur Tomaszewski, 2016. "Profitable areas in large-scale FTTH network optimization," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 61(3), pages 591-608, March.
    12. Baumgartner, Kerstin & Fuetterer, André & Thonemann, Ulrich W., 2012. "Supply chain design considering economies of scale and transport frequencies," European Journal of Operational Research, Elsevier, vol. 218(3), pages 789-800.
    13. Shang, Xiaoting & Zhang, Guoqing & Jia, Bin & Almanaseer, Mohammed, 2022. "The healthcare supply location-inventory-routing problem: A robust approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 158(C).
    14. Lo, Shirleen Lee Yuen & How, Bing Shen & Leong, Wei Dong & Teng, Sin Yong & Rhamdhani, Muhammad Akbar & Sunarso, Jaka, 2021. "Techno-economic analysis for biomass supply chain: A state-of-the-art review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 135(C).
    15. Funaki, Kenichi, 2012. "Strategic safety stock placement in supply chain design with due-date based demand," International Journal of Production Economics, Elsevier, vol. 135(1), pages 4-13.
    16. Melachrinoudis, Emanuel & Min, Hokey, 2000. "The dynamic relocation and phase-out of a hybrid, two-echelon plant/warehousing facility: A multiple objective approach," European Journal of Operational Research, Elsevier, vol. 123(1), pages 1-15, May.
    17. Leyla Ozsen & Collette R. Coullard & Mark S. Daskin, 2008. "Capacitated warehouse location model with risk pooling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(4), pages 295-312, June.
    18. Marianov, Vladimir & Eiselt, H.A., 2024. "Fifty Years of Location Theory - A Selective Review," European Journal of Operational Research, Elsevier, vol. 318(3), pages 701-718.
    19. Melachrinoudis, Emanuel & Min, Hokey, 2007. "Redesigning a warehouse network," European Journal of Operational Research, Elsevier, vol. 176(1), pages 210-229, January.
    20. Broek, John v.d. & Schutz, Peter & Stougie, Leen & Tomasgard, Asgeir, 2006. "Location of slaughterhouses under economies of scale," European Journal of Operational Research, Elsevier, vol. 175(2), pages 740-750, December.
    21. Franksen, Ole Immanuel & Grattan-Guinness, Ivor, 1989. "The earliest contribution to location theory? Spatio-economic equilibrium with Lamé and Clapeyron, 1829," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 31(3), pages 195-220.
    22. Hilmola, Olli-Pekka & Lorentz, Harri, 2010. "Warehousing in Europe - Northern actor perspective," European Transport \ Trasporti Europei, ISTIEE, Institute for the Study of Transport within the European Economic Integration, issue 45, pages 15-33.
    23. Ahmadi-Javid, Amir & Hoseinpour, Pooya, 2015. "A location-inventory-pricing model in a supply chain distribution network with price-sensitive demands and inventory-capacity constraints," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 82(C), pages 238-255.

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